On the recognition of k-equistable graphs

Vadim E. Levit, Martin Milanič, David Tankus

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations


A graph G∈=∈(V,E) is called equistable if there exist a positive integer t and a weight function such that S∈⊆∈V is a maximal stable set of G if and only if w(S)∈=∈t. The function w, if exists, is called an equistable function of G. No combinatorial characterization of equistable graphs is known, and the complexity status of recognizing equistable graphs is open. It is not even known whether recognizing equistable graphs is in NP. Let k be a positive integer. An equistable graph G∈=∈(V,E) is said to be k-equistable if it admits an equistable function which is bounded by k. For every constant k, we present a polynomial time algorithm which decides whether an input graph is k-equistable.

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 38th International Workshop, WG 2012, Revised Selcted Papers
Number of pages11
StatePublished - 2012
Event38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012 - Jerusalem, Israel
Duration: 26 Jun 201228 Jun 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7551 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference38th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2012


  • equistable graph
  • maximal stable set
  • polynomial time algorithm


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